Guarding scenes against invasive hypercubes

Authors:
Mark de Berg;Haggai David;Matthew J. Katz;Mark Overmars;A. Frank van der Stappen;Jules Vleugels
Affiliations:
Department of Computing Science, TU Eindhoven, PO Box 513, 5600 MB Eindhoven, The Netherlands;Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;Institute of Information and Computing Sciences, Utrecht University, PO Box 80.089, 3508 TB Utrecht, The Netherlands;Institute of Information and Computing Sciences, Utrecht University, PO Box 80.089, 3508 TB Utrecht, The Netherlands;Institute of Information and Computing Sciences, Utrecht University, PO Box 80.089, 3508 TB Utrecht, The Netherlands
Venue:
Computational Geometry: Theory and Applications
Year:
2003

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Abstract

In recent years realistic input models for geometric algorithms have been studied. The most important models introduced are fatness, low density, unclutteredness and small simple-cover complexity. These models form a strict hierarchy. Unfortunately, small simple-cover complexity is often too general to enable efficient algorithms. In this paper we introduce a new model based on guarding sets. Informally, a guarding set for a collection of objects is a set of points that approximates the distribution of the objects. Any axis-parallel hyper-cube that contains no guards in its interior may intersect at most a constant number of objects. We show that guardable scenes fit in between unclutteredness and small simple-cover complexity. They do enable efficient algorithms, for example a linear size binary space partition. We study properties of guardable scenes and give heuristic algorithms to compute small guarding sets.